The Z notation //, named after Zermelo–Fraenkel set theory, is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general.
In 1974, Jean-Raymond Abrial published "Data Semantics".1 He used a notation that would later be taught in the University of Grenoble until the end of the 1980s. While at EDF (Électricité de France), Abrial wrote internal notes on Z.citation needed The Z notation is used in the 1980 book Méthodes de programmation.2
Z was originally proposed by Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer.3 It was developed further at the Programming Research Group at Oxford University, where Abrial worked in the early 1980s, having arrived at Oxford in September 1979.
Z is based on the standard mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic. All expressions in Z notation are typed, thereby avoiding some of the paradoxes of naive set theory. Z contains a standardized catalog (called the mathematical toolkit) of commonly used mathematical functions and predicates.
- the standard is publicly available4 from the ISO ITTF site and available for purchase4 from the ISO site;
- the technical corrigendum is available5 from the ISO site free of charge.
- Espino, Luis, ERZ: Tool for to transform ER model to Z Notation equivalent.
- Community Z Tools (CZT) (project), Source forge.
- Z Word tools (project), Source forge for developing and checking Z specifications in Microsoft Word.
- Spivey, Michael ‘Mike’, Fuzz Type-Checker for Z.
- Z/Eves — A proof checker for the Z notation (German site but all manuals in English)
- Z/EVES Documentation, papers, and manuals on Z/EVES
- ZETA open-source system for development software specifications in Z
- HOL-Z open-source proof environment for Z in Isabelle/HOL
- CADiZ, a set of free software tools that assist use of Z notation
- ProofPower, a suite of open-source tools supporting specification and proof in HOL and in the Z notation
- Vimes An independently developed type checker.
- z-vimes Alternate source of Vimes.
- Z User Group (ZUG)
- Community Z Tools (CZT) project
- Other formal methods (and languages using formal specifications):
- Fastest is a model-based testing tool for the Z notation.
- Abrial, Jean-Raymond, "Data Semantics", in Klimbie; Koffeman, Data Base Management, North-Holland, pp. 1–59.
- Meyer, Bertrand; Baudoin, Claude (1980), Méthodes de programmation (in French), Eyrolles.
- Abrial, Jean-Raymond; Schuman, Stephen A; Meyer, Bertrand (1980), "A Specification Language", in Macnaghten, AM; McKeag, RM, On the Construction of Programs, Cambridge University Press, ISBN 0-521-23090-X (describes early version of the language).
- "ISO/IEC 13568:2002". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics (Zipped PDF). ISO. 2002-07-01. 196 pp.
- "ISO/IEC 13568:2002/Cor.1:2007" (PDF). Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics — Technical corrigendum 1. ISO. 2007-07-15. 12 pp.
- Spivey, John Michael (1992). The Z Notation: A reference manual. International Series in Computer Science (2nd ed.). Prentice Hall.
- Davies, Jim; Woodcock, Jim (1996). Using Z: Specification, Refinement and Proof. International Series in Computer Science. Prentice Hall. ISBN 0-13-948472-8.
- Bowen, Jonathan (1996). Formal Specification and Documentation using Z: A Case Study Approach. International Thomson Computer Press. ISBN 1-85032-230-9.
- Jacky, Jonathan (1997). The Way of Z: Practical Programming with Formal Methods. Cambridge University Press. ISBN 0-521-55976-6.